Find medial line or centerline

Hi, I wanted to find the MEDIAL or CENTER line from the attached image. It is somehow involve shrinking the internal boundary or expanding external boundary or vice versa. This image is derived from some morphological operations and ended with contour boundary extraction. My objective is to have a segmented image with single pixel drawing.

Really appreciate those who can help.

Original Image

Desired image (Center line that manually drawn)- * Here I just need the pink drawn line *